Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 58

The radius of tungsten is \(137 \mathrm{pm}\) and the density is \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\). Does elemental tungsten have a face-centered cubic structure or a body-centered cubic structure?

Short Answer

Expert verified
Elemental tungsten has a face-centered cubic (FCC) structure. This is determined by comparing the given density of tungsten \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\) to the theoretical densities of FCC and BCC structures. The theoretical density of the FCC structure is approximately \(19.546 \mathrm{~g} / \mathrm{cm}^{3}\) and the theoretical density of the BCC structure is approximately \(9.773 \mathrm{~g} / \mathrm{cm}^{3}\). Since the difference between the given density and the theoretical density of the FCC structure is smaller, we can conclude that elemental tungsten has a face-centered cubic (FCC) structure.

Step by step solution

01

Find the atomic mass of tungsten in grams

Using a periodic table, we find that the atomic mass of tungsten is 183.84 amu. To convert this to grams, we multiply by the atomic mass constant: Atomic mass of tungsten (in g/mol) = 183.84 amu * (1.660539 x 10^(-24) g/amu) = 305.43 x 10^(-24)g
02

Find the unit cell lattice parameter for tungsten

The unit cell lattice parameter is the distance between the centers of two atoms along the edge of the cube. For a cubic structure, we'll use the radius of the tungsten atom to calculate the lattice parameter. Radius of tungsten = 137 pm = 137 x 10^(-12) m For a cubic structure, unit_cell_edge_length = 2 * radius Unit cell lattice parameter (a) for tungsten = 2 * 137 x 10^(-12) m = 274 x 10^(-12) m
03

Calculate theoretical densities for FCC and BCC structures

The formula for theoretical density is: Theoretical Density = (n * atomic mass) / (volume of the unit cell * Avogadro's number) For FCC, n = 4 and for BCC, n = 2. Volume of the unit cell is given by: Volume = a^3 Where a is the unit cell lattice parameter. Theoretical density (FCC) = (4 * 305.43 x 10^(-24) g) / ((274 x 10^(-12) m)^3 * 6.022 x 10^23 atoms/mol * 10^6 cm^3/m^3) Theoretical density (BCC) = (2 * 305.43 x 10^(-24) g) / ((274 x 10^(-12) m)^3 * 6.022 x 10^23 atoms/mol * 10^6 cm^3/m^3) Theoretical density (FCC) ≈ 19.546 g/cm³ Theoretical density (BCC) ≈ 9.773 g/cm³
04

Compare theoretical densities with given density

Given density = 19.3 g/cm³ Comparing with the theoretical densities of FCC and BCC structures: Difference (FCC) = |19.546 - 19.3| ≈ 0.246 g/cm³ Difference (BCC) = |9.773 - 19.3| ≈ 9.527 g/cm³ Since the difference between the given density and the theoretical density of the FCC structure is smaller, we can conclude that elemental tungsten has a face-centered cubic (FCC) structure.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is an alloy? Explain the differences in structure between substitutional and interstitial alloys. Give an example of each type.

Identify the most important types of interparticle forces present in the solids of each of the following substances. a. \(\mathrm{BaSO}_{4}\) e. CsI b. \(\mathrm{H}_{2} \mathrm{~S}\) f. \(\mathrm{P}_{4}\) c. Xe g. \(\mathrm{NH}_{3}\) d. \(\mathrm{C}_{2} \mathrm{H}_{6}\)

What type of solid will each of the following substances form? a. \(\mathrm{CO}_{2}\) e. \(\mathrm{Ru}\) i. \(\mathrm{NaOH}\) b. \(\mathrm{SiO}_{2}\) f. \(\mathrm{I}_{2}\) j. \(\mathrm{U}\) c. Si g. \(\mathrm{KBr}\) k. \(\mathrm{CaCO}_{3}\) d. \(\mathrm{CH}_{4}\) h. \(\mathrm{H}_{2} \mathrm{O}\) 1\. \(\mathrm{PH}_{3}\)

Some ionic compounds contain a mixture of different charged cations. For example, wüstite is an oxide that contains both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) cations and has a formula of \(\mathrm{Fe}_{0.950} \mathrm{O}_{1.00} .\) Calculate the fraction of iron ions present as \(\mathrm{Fe}^{3+}\). What fraction of the sites normally occupied by \(\mathrm{Fe}^{2+}\) must be vacant in this solid?

The second-order diffraction \((n=2)\) for a gold crystal is at an angle of \(22.20^{\circ}\) for \(X\) rays of 154 pm. What is the spacing between these crystal planes?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Inorganic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free